SF6 total columns were successfully retrieved from FTIR (Fourier transform infrared)
measurements (Saint Denis and Maïdo) on Reunion Island
(21∘ S, 55∘ E) between 2004 and 2016 using the SFIT4
algorithm: the retrieval strategy and the error budget were
presented. The FTIR SF6 retrieval has independent
information in only one individual layer, covering the whole of the
troposphere and the lower stratosphere. The trend in SF6 was
analysed based on the FTIR-retrieved dry-air column-averaged mole
fractions (XSF6) on Reunion Island, the in situ
measurements at America Samoa (SMO) and the collocated satellite
measurements (Michelson
Interferometer for Passive Atmospheric Sounding, MIPAS, and Atmospheric Chemistry Experiment Fourier Transform Spectrometer, ACE-FTS) in the southern tropics. The
SF6 annual growth rate from FTIR retrievals is
0.265±0.013pptv year−1 for 2004–2016, which is slightly
weaker than that from the SMO in situ measurements
(0.285±0.002pptv year−1) for the same time period. The
SF6 trend in the troposphere from MIPAS and ACE-FTS
observations is also close to the ones from the FTIR retrievals and
the SMO in situ measurements.

Sulfur hexafluoride (SF6) is very stable in the atmosphere
and is well-mixed and one of the most potent greenhouse gases listed
in the 1997 Kyoto protocol linked to the United Nations Framework
Convention on Climate Change (UNFCCC). It has an extremely long
lifetime of 850 years (Ray et al., 2017) with global warming
potential for a 100-year time horizon of 23 700 (relative to
CO2) (Kovács et al., 2017). Since SF6 is a very stable
trace gas in the atmosphere and its annual growth rate seems
relatively constant during the last two decades (Hall et al., 2011),
it is usually applied to calculate the age of air
(Patra et al., 1997; Engel, 2002; Patra et al., 2009; Stiller et al., 2012; Haenel et al., 2015).

Figure 1Time series of historical and projected global SF6 emissions. Historical data cover 1900–2005 (black), and projections for the 2005–2100 time period correspond to four RCP scenarios with 2.6, 4.5, 6.0 and 8.5 W m−2 radiative forcing in 2100 relative to pre-industrial values (Moss et al., 2010). The black dot is the annual growth of SF6 in 2012 according to the WMO report (WMO, 2014).

SF6 is emitted from anthropogenic sources at the Earth's
surface, mainly from the chemical industry, such as in production of
electrical insulators and semi-conductors, and magnesium
manufacturing. The mole fraction of SF6 in the atmosphere
has increased in recent years and the globally averaged
near-surface SF6 volume mixing ratio (VMR) has reached up
to 7.6 pptv (parts per trillion by volume), with an annual
increase of 0.3 pptv year−1 in 2012
(WMO, 2014). Figure 1 shows the SF6 historical global emissions in
1900–2005 (Schultz et al., 2008; Mieville et al., 2010). Emissions of
SF6 started in the 1940s and have been increasing since
then. Only during 1990–2000 the emissions almost remain
constant. The most likely reason is that SF6 emissions
decreased in developed countries between 1995 and 1998 but then
increased again after 1998 (Levin et al., 2010; Rigby et al., 2010). The
SF6 global total emissions in 2005 were
6.341 Gg year−1 (1 Gg=1000 t), which is
about 8 times larger than that in 1970
(0.789 Gg year−1). Figure 1 also shows the predictions of
SF6 global emissions for 2005–2100 according to four
representative concentration pathway (RCP) scenarios with
different radiative forcing values (2.6, 4.5, 6.0 and
8.5 W m−2) in 2100 relative to pre-industrial values
(Moss et al., 2010). The RCP 6.0 and RCP 8.5 scenarios assume the
emissions keep increasing until 2020 and 2100 respectively, while
RCP 2.6 and RCP 4.5 scenarios assume that there will be a steep
decrease after 2010. The predictions from these four scenarios are
very different, so it is very important to monitor the
abundance of SF6 in the atmosphere. The most recent
Scientific Assessment of Ozone Depletion report
(WMO, 2014) points out that the
global emissions have amounted to 8.0 Gg year−1 in 2012,
marked by a black dot in Fig. 1.

The Advanced Global Atmospheric Gases Experiment (AGAGE) gas
chromatography–mass spectrometry (GC–MS) system has
measured the SF6 concentration since 1973
(Rigby et al., 2010). The Halocarbons and other Atmospheric Trace
Species Group (HATS) started SF6 sampling measurements at
eight stations in 1995 and in situ measurements at six fixed sites
in 1998 (Hall et al., 2011). The flask and in situ measurements show
that the SF6 abundance in the atmosphere has been
increasing since the 1970s
(Maiss and Levin, 1994; Geller et al., 1997; Maiss and Brenninkmeijer, 1998; Moss et al., 2010). In recent
decades, remote sensing techniques also contribute to monitoring
SF6. Rinsland et al. (1990) used the spectra observed by the
Atmospheric Trace Molecule Spectroscopy instrument (ATMOS) aboard
the space shuttle, as part of the Spacelab 3 (SL3) payload, to
retrieve SF6 concentrations in the upper troposphere and
lower stratosphere. In addition, space-based sensors, such as the
Atmospheric Chemistry Experiment Fourier Transform Spectrometer
(ACE-FTS) (Bernath et al., 2005; Bernath, 2017) and the Michelson
Interferometer for Passive Atmospheric Sounding (MIPAS)
(Stiller et al., 2008), are applied to obtain an SF6 global
distribution and trend. Zander et al. (1991) succeeded in monitoring
the increasing total column of SF6 using the ground-based
Fourier transform infrared spectrometer (FTIR) at Jungfraujoch
(46.55∘ N, 7.98∘ E,
3.58 kma.s.l.). Later on, Rinsland et al. (2003) and
Krieg et al. (2005) obtained the total columns of SF6 from
the FTIR measurements at Kitt Peak (31.9∘ N,
111.6∘ W, 2.09 kma.s.l.) and Ny-Ålesund
(78.91∘ N, 11.88∘ E,
0.02 kma.s.l.). They found that the mixing ratio of
SF6 is continuously increasing and that the mean increases
of SF6 are 0.31±0.08pptv year−1 at
Ny-Ålesund, 0.24±0.01pptv year−1 at Jungfraujoch
and 0.28±0.09pptv year−1 at Kitt Peak from March 1993
to March 2002. In the latest Scientific Assessment of Ozone
Depletion, the trends of SF6 from in situ measurements are
consistent with the trends in the troposphere from remote sensing
measurements (ACE-FTS, MIPAS and Jungfraujoch FTIR)
(WMO, 2014).

Figure 2The typical spectrum of SF6 retrieval microwindows (946.5–949.0 cm−1) at St Denis (a)
and Maïdo (b). The bottom panels list the absorption contribution from each species. To clarify
the absorption lines, the transmittance is shifted by 0.02 for each species and the solar (sol) line list. The
middle panels only show the transmittance between 0.95 and 1.05 and identify the SF6 absorption line.
The top panels show the transmittance residual (observed minus calculated).

The objective of this paper is to investigate the SF6
retrievals in the southern tropics based on the spectra observed
by two FTIR spectrometers on Reunion Island (21∘ S,
55∘ E) from 2004 to 2016. In Sect. 2, SF6
retrievals are carried out with the well-established SFIT4
algorithm, which is upgraded from the radiative transfer and
retrieval algorithm SFIT2 (Pougatchev et al., 1995; Hase et al., 2004) and
widely used in the Network for the Detection of Atmospheric
Composition Change Infrared Working Group (NDACC-IRWG)
community. The FTIR SF6 retrieval strategy and the error
budget are discussed in detail. In the following section, the
trend in SF6 is analysed based on the FTIR retrievals, the
HATS America Samoa (SMO) in situ measurements (14∘ S,
170∘ W, 77 ma.s.l.) and the collocated
satellite measurements (MIPAS and ACE-FTS). Finally, conclusions
are drawn in Sect. 4.

The Royal Belgian Institute for Space Aeronomy operates at two FTIR
sites on Reunion Island. One is at Saint Denis (St Denis), close
to the coast (20.90∘ S, 55.48∘ E; 85 m
a.s.l.), and the other one is located at the Maïdo mountain site
(21.07∘ S, 55.38∘ E; 2155 m a.s.l.). At
present, both sites are equipped with a Bruker 125HR spectrometer,
a precise solar-tracker system and an automatic weather
station. The St Denis FTIR is dedicated to the near-infrared
spectral region and has contributed to the Total Carbon Column
Observing Network (TCCON) since September 2011, whereas the
Maïdo FTIR is dedicated to the mid- to thermal infrared
spectral region and has become an NDACC-IRWG instrument in March
2013. Before September 2011, a Bruker 120M instrument was operated
at St Denis in the NDACC mid- to thermal infrared
configuration. For detailed information about the two sites, please
refer to Zhou et al. (2016) and the references therein.

The SF6 retrievals use the spectra in the thermal infrared
range. Therefore, we select the spectra from the Bruker 120M at St
Denis (2004–2011) and from the Bruker 125HR at Maïdo
(2013–2016).

The spectra of 700–1400 cm−1 at St Denis and Maïdo
are recorded with the same settings. Two maximum optical path
differences (MOPDs) of 82 and 125 cm are operated to gather
the interferogram of the direct solar radiation, and then the
interferogram is transformed to a spectrum with the spectral
resolutions of 0.010975 and 0.0072 cm−1 through a fast
Fourier transform (FFT) algorithm. The HgCdTe (MCT) detector
collects the spectrum and one specific interference filter is used
to narrow the optical band to regions of interest in order to
improve the signal-to-noise ratio (SNR).

2.1 Retrieval strategy

We used the SFIT4_v9.4.4 algorithm (Pougatchev et al., 1995) to
retrieve information from the spectra: it simulates the spectrum
observed by the ground-based FTIR and looks for the optimum state
vector (the retrieved state) to minimise the residual between the
simulated and the observed spectra. Table 1 lists the retrieval
window, interfering gases, spectroscopic database, a priori
profile, background parameters and SNR used in the SFIT4 algorithm
for the SF6 retrieval at St Denis and Maïdo, together
with the obtained degrees of freedom of signal (DOFS).

2.1.1 Retrieval window

The broad unresolved Q branch of the ν3 band of SF6,
at 947.9 cm−1(Varanasi et al., 1992), is always used to
retrieve SF6 by remote sensing
techniques. Zander et al. (1991) used 946.9–948.9 cm−1 for
the FTIR retrieval at Jungfraujoch and Krieg et al. (2005) used
947.2–948.6 cm−1 for Kitt Peak and Ny-Ålesund FTIR
retrievals. We also used the SF6 absorption line at
947.9 cm−1 and the retrieval window
946.5–949.0 cm−1 to perform the FTIR retrieval at
Reunion Island. However, compared with the previous studies,
our retrieval window contains an additional weak H2O
absorption line at 946.68 cm−1. Since there is a strong
H2O absorption line at 948.26 cm−1 and a strong
CO2 line at 947.74 cm−1 (see
Fig. 2), the SF6 is inevitably influenced by these
two species, especially from H2O due to its larger
variability in the atmosphere. A better fitting of H2O
(with a smaller root mean square (rms) of the fitting residual) is
obtained by the larger retrieval window. In addition, to minimise
interference from H2O and CO2, their profiles are
retrieved simultaneously with the SF6 profile.

2.1.2 Instrument line shape

In order to acquire the instrument line shape (ILS) and to verify
the alignment of the instrument, daily HBr cell measurements are
carried out automatically at both sites. The LINEFIT14.5 programme
(Hase et al., 1999) is applied to obtain the modulation and phase
parameters of the ILS, which are used as input to the SFIT4
algorithm. Note that we made a 3-order polynomial fitting from the
LINEFIT outputs and then retrieved the polynomial parameters in
SFIT4 algorithm for both modulation and phase.

2.1.3 Spectroscopy

The spectroscopy of SF6 was taken from the pseudo-line
lists (http://mark4sun.jpl.nasa.gov/pseudo.html), and the
spectroscopy of the other species was obtained from the ATM16
line lists (Toon, 2014). Pseudo-line lists were produced by
Geoff Toon (NASA-JPL) by fitting all the laboratory spectra
simultaneously, which includes mean intensities and effective lower
state energies on a 0.005 cm−1 frequency grid. These
artificial lines at arbitrary positions do not represent
transitions of molecules. Instead, their line-widths and
intensities are fitted to the laboratory spectra such that the
pseudo-line lists allow to simulate the measured spectra.

2.1.4 A priori profile

To construct an a priori profile that is close to the true one, we used
the US standard atmosphere (1976) SF6(National Geophysical Data Center, 1992) as the shape of the
a priori profile, and then scaled it with a factor of one to make the
concentration of the lowest level equal to the annual mean of SMO
measurements in 2009. The H2O a priori profile was derived
from the 6-hourly NCEP reanalysis data. For the a priori profiles
of the other interfering species (see Table 1), the mean of the
Whole Atmosphere Community Climate Model (WACCM) version 6 monthly
profiles between 1980 and 2020 were adopted.

2.1.5 Regularisation matrix

The a priori covariance matrix, together with the measurement noise
covariance matrix, determine the weights of a priori knowledge and
measurement information (Rodgers, 2000). The SNR were set to
180 and 400 at St Denis and Maïdo, respectively. In order to
extract as much information as possible from the measurements and
to avoid too many oscillations in the retrieved SF6
profiles, we used 30 and 14 % as the diagonal elements
(the same value for all levels) to create the regularisation
matrices at St Denis and Maïdo, respectively. The correlation
width was set to 10.0 km. Note that the diagonal value of
the regularisation matrix is a key parameter that balances the
contribution from the measurement information and the a priori
information, but does not represent the real variability of
SF6 in the atmosphere.

2.1.6 Averaging kernel

Figure 3 shows the typical averaging kernel of the SF6
retrieval at Maïdo. The FTIR retrieval is sensitive to the
altitude range from the surface to 20 km (the whole of the
troposphere and lower stratosphere). The mean and standard
deviations of the DOFS of the SF6 retrievals are 1.0±0.1
at St Denis and 1.1±0.1 at Maïdo, indicating that the
SF6 retrievals have information content in only one
individual layer (mainly 0–20 km) and have no profile
information. That means the retrieved profiles are not reliable,
and we should focus on the total column. In this study, the
SF6 retrievals at St Denis were combined with Maïdo
retrievals to extend the time coverage for the trend in
Sect. 3. The DOFS at the two stations are very similar, and there is
no observed trend in the time series of the DOFS.

Figure 3The typical averaging kernel of SF6 retrieval at Maïdo. The solid lines
represent the sensitivities at specific altitudes. The red dashed line is the sum
of the rows of averaging kernels scaled by 0.1, indicating the vertical sensitivity.

2.2 Error budget

Based on the optimal estimation method (Rodgers, 2000), the
difference between the retrieved state vector x^ and
the true state vector xt could be expressed as

x^-xt=(A-I)(xt-xa)(1)+GyKb(bt-b)+GyΔf+Gyεy,

where xa is the a priori state vector;
A is the averaging kernel matrix, representing the
sensitivity of the retrieved state vector to the true state vector;
I is a unit matrix; Gy is the contribution
matrix, representing the sensitivity of the retrieval to the
measurement y; Kb is the weight function,
representing the sensitivity of the forward model
F(x,b) to the forward model parameters; b is
the vector of forward model parameters that are not retrieved;
bt is the vector of true forward model
parameters; Δf is the forward model
systematic uncertainty; εy is the measurement
noise covariance matrix. Note that the state vector x,
which is the vector of forward model parameters that are retrieved,
is a higher-dimensional vector which consists of the
target SF6 profile components, the concentration profiles
for the interfering species (H2O, CO2) and other
retrieval parameters (slope, ILS, etc.).

The error in the target SF6 profile is obtained by
extracting the SF6 components from the vectorial equation
in Eq. (1). The error in the retrieved SF6 profile
(x^-xt)SF6 then
consists of the smoothing error
(A-I)(xt-xa),
model parameter error GyKb(bt−b), forward model error GyΔf and measurement noise Gyεy. As the SFIT4 algorithm is well established
and only the physics of the absorption is included in the
transmission of radiation, the forward model error can be ignored.

Table 1The retrieval window, interfering gases, spectroscopic database, a priori profile,
background parameters (slope and zshift) and SNR used in the SFIT4 algorithm for FTIR SF6
retrieval at St Denis and Maïdo, together with the achieved DOFS (mean and the standard deviation) of the retrievals.

The smoothing error, except for the uncertainty from
SF6, also includes the uncertainties from the
H2O profile, the CO2 profile, the C2H4 and
O3 scaling factors and some other parameters (see Table 1),
and is defined as the retrieval parameter error
εre. Since the absorption lines of
H2O and CO2 are very strong in the retrieval
window, the εre is separated into three
components.

where ASF6,SF6,
ASF6,H2O,
ASF6,CO2 and
ASF6,others are the matrices extracted
from the full averaging kernel A by selecting the
components Aij where the row index i runs over all
SF6 components in the state vector x and the column
index j runs over all SF6, H2O, CO2 and
other components in state vector
x. xt,SF6 and
xa,SF6,
xt,H2O and
xa,H2O,
xt,CO2 and
xa,CO2,
xt,others and
xa,others are the true and a priori values
of SF6, H2O, CO2 and other retrieval
parameters.

Systematic and random components are considered to characterise the
uncertainty of each parameter. For the smoothing error
(ASF6,SF6-I)(xt,SF6-xa,SF6),
we assumed that the systematic uncertainty of
ε(xt,SF6-xa,SF6)
is 5 % relative to the a priori profile
(σSF6,ai=0.05xai). Then, the diagonal
and off-diagonal values of the systematic part of
ε(xt,SF6-xa,SF6)(xt,SF6-xa,SF6)T
are calculated as (σSF6,ai2) and
σSF6,aiσSF6,aj, respectively
(von Clarmann, 2014). The random part of
ε(xt,SF6-xa,SF6)(xt,SF6-xa,SF6)T
is constructed in the same way as the regularisation matrix but the diagonal
elements were set to 30 % for both St Denis and
Maïdo. For the measurement error Gyε, there is no systematic uncertainty and
the random uncertainty is derived from the SNR.

For the εre, we mainly focus on the
influence from H2O and CO2. The systematic and the
random uncertainties of the H2O profile were derived from the
bias and the standard deviation of the differences between the NCEP
profiles and the balloon sondes. In general, the systematic
uncertainty is about 5 % and the random uncertainty is about
10 % from surface to 10 km. The CO2
systematic uncertainty is assumed to be 5 % of the average
of the WACCM monthly profiles, and the random uncertainty is the
standard deviation of the WACCM monthly profiles from 1980 to 2020.

Table 2The systematic and random uncertainties for the FTIR-retrieved total column (%) at St Denis and Maïdo. σb are the relative systematic (random) uncertainties of the non-retrieved parameters (%). The “retrieval parameters” represents the “others” in Eq. (3). The SF6 spectroscopy uncertainty is from the pseudo-line database. When a relative uncertainty is smaller than 0.1 %, it is considered negligible and represented as “–”.

For the model parameter error GyKb(bt−b), we only show the significant
parameters here, i.e. temperature, spectroscopy, solar zenith angle
(SZA), ILS and zero level offset (zshift). The systematic and
random uncertainties of the temperature profile were derived from
the mean and the standard deviation of the differences between the
NCEP profiles and the balloon sondes on Reunion Island in
2011. In general, the systematic bias is about 5 K below
10 km, 3 K between 10 and 15 km and
1 K above 15 km. The standard deviation is about
2–4 K in the troposphere and 5–10 K above tropopause
height. The SF6 spectroscopy uncertainty is from the pseudo
database: 2 % for the systematic part and zero for the
random part. Values of 0.1 and 0.2 % were adopted for the systematic
and random uncertainties of SZA according to the Pysolar package
(one Python code to calculate the solar position
http://pysolar.org/), while 5 and 1 % were adopted for
both systematic and random uncertainties of the ILS parameters and
zshift, respectively.

Table 2 lists the SF6 FTIR retrieval systematic and
random uncertainties (%) at St Denis and Maïdo. The
“retrieval parameters” in Table 2 represents the “others”
in Eq. (3). The smoothing error, measurement error, H2O
interference and temperature error at St Denis are much larger than
those at Maïdo. In total, the retrieval systematic and random
uncertainties (relative to the retrieved SF6 total
column) are 4.6 and 14.0% at St Denis and
3.7 and 6.7% at Maïdo, respectively.

3.1 Data sets

3.1.1 SMO in situ measurements

Since 1998, a four channel gas chromatograph (CATS) system has been
measuring the surface SF6 at the SMO site. Due to the high
accuracy and precision, the CATS SF6 daily data from the
NOAA ESRL halocarbon in situ measurement programme are considered to
be a reference for comparison with the FTIR retrievals. Note that
these are daily median data instead of daily means and are used to
filter the higher outliers from local pollution. As there is an
improvement in the instrument in June 2000, the standard deviation
of 1-day measurements decreased from 0.2 to 0.4 to
0.02–0.04 pptv after the change (Hall et al., 2011).

3.1.2 MIPAS

MIPAS derived the global distributions of profiles of SF6
from limb observations between 2002 and 2012. MIPAS observed
spectra in full spectral resolution (FR) mode (spectral resolution:
0.05 cm−1) and reduced resolution (RR) mode (spectral
resolution: 0.121 cm−1) before and after January
2005. In this paper, we used the latest SF6 product with
newly calibrated level 1b spectra (Haenel et al., 2015) to compare it
with the FTIR retrievals and to make the SF6 trend
analysis. The SF6 data used here are versions V5h_SF6_20
for the FR data product and V5r_SF6_222 and V5r_SF6_223 for the
RR period. The MIPAS retrievals cover the upper troposphere (down
to cloud top, or ∼6km in cloud-free cases) and the
stratosphere only (about 55 km; see Fig. 7). Since MIPAS
single SF6 profiles are very noisy, we used the monthly
means in the latitude band of 20–25∘ S.

3.1.3 ACE-FTS

Global distributions of SF6 are also monitored by ACE-FTS
occultation measurements from 2004 (Boone et al., 2013). We used the
ACE-FTS level 2 version 3.5 monthly data (2004–2013) from the
ACE/SCISAT database, and only the measurements without any known
issues (quality flag = 0) were selected (Sheese et al., 2015). The
ACE-FTS data have been validated with MkIV balloon profiles
(Velazco et al., 2011). Since ACE-FTS mainly look at the polar area,
there are few measurements in the tropical zone. Geller et al. (1997)
found that SF6 is well mixed throughout the Southern
Hemisphere; therefore, we enlarged the latitude band for ACE-FTS
measurements to 0–40∘ S to get a robust result. Similar
to MIPAS measurements, ACE-FTS collects the spectra in the upper
troposphere and stratosphere (about 10–30 km; see Fig. 7).

Figure 4The locations of the ground-based sites (Reunion Island and SMO) as well as the latitude bands covered by the satellites (MIPAS and ACE-FTS).

3.1.4 Ground-based FTIR

As the FTIR SF6 retrievals have only one layer of
information, we applied the dry-air column-averaged SF6
(XSF6) of FTIR measurements to quantitatively compare it
with other data sets. XSF6 is obtained by dividing the
SF6 total column by the dry-air total column.

(4)XSF6=TCSF6TCairdry,(5)TCairdry=Psgmairdry-TCH2OmH2O/mairdry,

where TCSF6 and
TCairdry are the
total columns of SF6 and dry air; Ps is the surface
pressure; g is the acceleration of gravity depending on the
latitude and altitude; and mH2O and mairdry
are the molecular masses of H2O and dry air, respectively;
TCH2O is the total column of H2O from NCEP
re-analysis data. The surface pressure is recorded with a Vaisala
PTB210 sensor, with accuracy better than 0.1 hPa. The
systematic uncertainty of H2O in the troposphere is about
5 %, and the TCH2O on Reunion Island is about
1–2 % of the TCair. As a result, the
uncertainty of the TCairdry is better than
0.1 %.

Note that the SF6 concentration is almost constant in the
troposphere but much lower in the stratosphere. This kind of
profile will lead to a systematic bias if we combine
theXSF6 in 0–100 km (above St Denis) and
XSF6 in 2.155–100 km (above Maïdo)
directly. To avoid this systematic bias, we kept the
XSF6 at St Denis unchanged and applied a scaling
factor of 1.01 to the XSF6 at Maïdo, which is the
ratio of XSF6 in 0–100 km to
XSF6 in 2.155–100 km based on the FTIR
SF6 a priori profile but scaled with the annual mean of SMO
in situ measurements in 2014.

Figure 6SF6 annual growths from SMO in situ measurements (2004–2016) (blue bar), ground-based FTIR measurements (2004–2016: combined St Denis and Maïdo)(pink bar), MIPAS measurements (2002–2012) in the latitude band of 20–25∘ S for different altitudes (9–52 km) (black solid line) and ACE-FTS measurements (2004–2013) in the latitude band of 0–40∘ S for an altitude range of 10.5–32.5 km (brown solid line). For MIPAS and ACE-FTS measurements, the dotted line of the same colour is the number of monthly means used for trend analysis at each altitude.

Figure 4 shows the locations of the ground-based observations and
the latitude bands covered by the satellites. The SF6 time
series of SMO in situ, MIPAS and ACE-FTS measurements and FTIR
retrievals at St Denis and Maïdo are presented in Fig. 5. For
MIPAS, ACE-FTS and FTIR data, the error bar is the standard
deviation of all the measurements in 1 month. Since the FTIR
retrieval has the largest sensitivity in the vertical range of
5–15 km (see Fig. 3), we selected 11 km of
MIPAS and 12.5 km of ACE-FTS. In general, SF6
from these data sets are in good agreement, as the difference
between each two measurements is within their uncertainties.

where Y(t) is measurements with the t in fraction
of year; A0 is the intercept; A1 is the annual growth;
A2 to A7 are the periodic variations, mainly representing
the seasonal cycle; ε(t) is the
residual between the measurements and the fitting model. To
estimate the trend error σc, the autocorrelation
of the residual should be taken into account (Santer et al., 2000).

(7)σc=σd(n-2)[n(1-r)/(1+r)-2],

where σd is the regression error; n is the
number of measurements; and r is the lag-1 (1 month)
autocorrelation coefficient of the regression residuals.

Figure 7SF6 monthly means of volume mixing ratios profiles (a, b) and
the number of measurements in each month (c, d) for MIPAS in the
latitude band between 20 and 25∘ S (a, c) and ACE-FTS in the
latitude band between 0 and 40∘ S (b, d).

3.3 Annual change

Figure 6 shows the SF6 trends from the SMO in situ
measurements, the ground-based FTIR retrievals, the MIPAS
measurements in the latitude band of 20–25∘ S for
different altitudes (9–52 km), and the ACE-FTS
measurements in the latitude band of 0–40∘ S for altitude
range of 10.5–32.5 km. The vertical sensitivity of the
FTIR retrieval is between the surface and 20 km (see
Fig. 3). For MIPAS and ACE-FTS measurements, Fig. 6 also shows the
number of monthly means used for the trend analysis at each
altitude (dotted lines). The annual growth of FTIR measurements is
0.265±0.013pptv year−1 from 2004 to 2016, which is
slightly weaker than the trend in the SMO in situ measurements
(0.285±0.002pptv year−1) for the same time
period. Waugh et al. (2013) pointed out that the age of near-surface
SF6 at SMO (14∘ S) is about 0.4 years higher than
that on Reunion Island (21∘ S). In addition, the
global surface in situ measurement network
(https://www.esrl.noaa.gov/gmd/hats/combined/SF6.html) shows
that the growth rate of SF6 slightly increases with
time. Therefore, it is acceptable that the trends from FTIR
measurements on Reunion Island are slightly weaker than those
from the SMO in situ measurements.

The trend uncertainty from MIPAS data is less than from the ACE-FTS data
and the FTIR retrievals because MIPAS has many more data
points. The profile of SF6 trend shows a peak at
altitude of 11–13 km from the MIPAS measurements, and a peak
at 11.5–16.5 km from the ACE-FTS measurements. As the
SF6 emissions are all at the Earth's surface and there is
almost no removal mechanism in the troposphere and stratosphere
(Kovács et al., 2017), the SF6 concentration should be
well mixed in the troposphere (the tropopause height above
Reunion Island is about 16.5 km) and decreases above
the tropopause, which was confirmed by the airborne in situ
measurements (Patra et al., 1997). Figure 7 shows the SF6
monthly means and the number of measurements in each month from
MIPAS and ACE-FTS. The numbers of good quality measurements at
9 km for MIPAS and 10.5 km for ACE-FTS are
considerably reduced because a large number of measurements are
contaminated by clouds. As a consequence, the trends at these
altitudes from MIPAS and ACE-FTS were derived from a small number
of measurements, leading to larger uncertainties. For example, in
October 2004, there are only three ACE-FTS measurements within the
latitude band range 0–40∘ S, and the SF6 monthly
mean at 10.5 km is 7.57 pptv, which is very large
compared with the monthly means in November 2004 (4.92) and December(5.80 pptv).

In general, the SF6 trend from the SMO in situ measurements
at surface or from the FTIR retrievals is close to the trends at
the troposphere from the MIPAS and ACE-FTS measurements. In the
stratosphere, satellite measurements (both MIPAS and ACE-FTS) show
that the SF6 trend decreases with increasing altitude. The
change in the SF6 trends in the stratosphere could be
applied to estimate how long it takes for the well-mixed air mass
to transport from the surface to the high altitude on a large scale
(Waugh, 2002; Stiller et al., 2012).

The SF6 total columns were retrieved with the SFIT4 algorithm
from two FTIRs on Reunion Island (21∘ S,
55∘ E) in 2004–2016. The FTIR SF6 retrieval is
sensitive to the whole troposphere and lower stratosphere but has
only 1 degree of freedom. We used the retrieval window
(946.5–949.0 cm−1) for the SF6 retrieval at
St Denis and Maïdo, with the broad unresolved Q branch of the
ν3 band of SF6, at 947.9 cm−1. Nearby are
a strong H2O absorption line at 948.26 cm−1,
a weak H2O absorption line at 946.68 cm−1 and
a strong CO2 line at 947.74 cm−1. The
SF6 retrieval product is influenced by these two species,
especially by H2O due to its larger variability in the
atmosphere. The retrieval window in this study is wider than the
previous ones (Zander et al., 1991; Krieg et al., 2005) because for the humid
sites, such as St Denis, a better fitting is obtained with the
larger window.

To estimate the SF6 retrieval error, four components (the
smoothing error, forward model parameter error, measurement error
and other retrieval parameter errors) have been discussed in
detail. In total, the systematic and random uncertainties of the FTIR-retrieved
SF6 columns are 4.6 and 14.0 % at St Denis
and 3.7 and 6.7% at Maïdo. Both systematic and random
uncertainties at St Denis are larger than those at Maïdo,
because of the lower SNR and the higher water vapour abundance at
St Denis.

The trend in XSF6 derived from FTIR measurements is
0.265±0.013pptv year−1 for 2004–2016, which is
slightly weaker than the trend from the SMO in situ measurements
(0.285±0.002pptv year−1) for the same time
period. The SF6 trends at 9 km from MIPAS
measurements and 10.5 km from ACE-FTS measurements are
rather uncertain due to scarceness of data, because the MIPAS and
ACE-FTS measurements are contaminated by cumulus clouds at low
altitudes and these values are not included for the trend
calculation. The SF6 trends in the troposphere from both
MIPAS and ACE-FTS measurements are close to the trends from FTIR
retrievals and SMO in situ measurements; the SF6 trends
from MIPAS and ACE-FTS above the tropopause height decrease with
increasing altitude.

The FTIR SF6 retrievals on Reunion Island (St Denis and Maïdo) are not
publicly available yet. To obtain access to site data, please contact the author or the
BIRA-IASB FTIR group. The MIPAS SF6 data are provided by the MIPAS satellite
group at KIT/IMK, please contact Gabriele Stiller (gabriele.stiller@kit.edu).
The ACE-FTS data used in this study
are available from https://ace.uwaterloo.ca/
(registration required). SMO in situ SF6 measurements are
publicly available ftp://ftp.cmdl.noaa.gov/hats/sf6/insituGCs/CATS/daily/ (NOAA, 2018).

The authors thank the National Basic Research Programme of China
(2013CB955801), the National Natural Science Foundation of China
(41575034), the Belgian Science Policy for financial support through
the supplementary researchers programme and the AGACC projects
(SD/AT/01A) and (SD/CS/07A) in the Science for Sustainable
Development programme. They wish to thank the Université de la
Reunion, in particular Jean-Marc Metzger (UMS3365 of the OSU
Reunion) as well as the French regional and national (INSU,
CNRS) organisations, for supporting the NDACC operations in Reunion
Island. We also want to thank Geoff Toon (JPL) for providing the
spectroscopy. The Atmospheric Chemistry Experiment (ACE), also known
as SCISAT, is a Canadian-led mission mainly supported by the
Canadian Space Agency and the Natural Sciences and Engineering
Research Council of Canada. MIPAS SF6 data were derived
within research projects funded by the “CAWSES” priority programme
of the German Research Foundation (DFG) (project STI 210/5-3) and
the“ROMIC” programme of the German Federal Ministry of Education
and Research (BMBF) (project
01LG1221B).

Engel, A.: Temporal development of total chlorine in the high-latitude stratosphere based on reference distributions of mean age derived from CO2 and SF6, J. Geophys. Res., 107, 4136, https://doi.org/10.1029/2001JD000584, 2002. a

SF6 total columns are successfully retrieved from FTIR measurements (Saint Denis and Maïdo) at Reunion Island (21° S, 55° E) between 2004 and 2016 using the SFIT4 algorithm: the retrieval strategy and the error budget are discussed. The trend of SF6 is analysed based on the FTIR retrievals at Reunion Island, the in situ measurements at America Samoa (SMO) and the collocated satellite measurements (MIPAS and ACE-FTS) in the southern tropics. The results show good agreement.